Fractional excitations in cold atomic gases

We study the behavior of excitations in the tilted one-dimensional Bose-Hubbard model. In the phase with broken symmetry, fundamental excitations are domain walls which show fractional statistics. Using perturbation theory, we derive an analytic model for the time evolution of these fractional excitations, and demonstrate the existence of a repulsively bound state above a critical center-of-mass momentum. The validity of the perturbative analysis is confirmed by the use of time-adaptive density-matrix renormalization group simulations. These findings open the path for the experimental detection of fractional particles in cold atomic gases.